The Assembly and Classification of the Elements Using the Roberts-Janet Nuclear Periodic Table
Total Page:16
File Type:pdf, Size:1020Kb
Research Article Journal of Volume 9:1, 2020 DOI: 10.37421/jme.2020.9.549 Material Sciences & Engineering ISSN: 2169-0022 Open Access The Assembly and Classification of the Elements Using the Roberts-Janet Nuclear Periodic Table John O Roberts* Researcher, Former Open University Tutor, UK Abstract A framework and surprisingly coherent analysis of the elements is presented using the Roberts-Janet table derived by inverting the Periodic Table coupled with the Quantum Mechanical Table established using the mathematics of the Standard Model and groups U (1) x S U (2) x S U (3). Having already identified in previous articles a one to one mapping between the two tables, this article seeks to consolidate such a framework to include nucleosynthesis by presenting the appearance of the highly stable numbers of neutrons and protons – magic numbers within the Nuclear Shell Model – as a consequence of the framework itself. The article also seeks to illustrate similarities between the electron structure of individual elements in condensed matter (Periodic Table) and the structure of neutrons and protons in plasma during fusion (Nucleosynthesis) and its possible extension to the Standard Model and beyond. Phase changes together with suitable boundary conditions lead to the hypothesis that all elements ultimately become metallic. Keywords: Periodic table • Isotopes • Spectral energy • Quantum number Historic and Current Framework to the Saxon-Woods model a reasonable agreement with observed binding energies is obtained. The Periodic Table crystallized in 1869 via Dmitri Mendeleev from Configurations of 2, 8, 20, 28, 50, 82 and 126 protons and neutrons the experimental and theoretical discoveries of new elements and the separately give rise to larger binding energies, spherical configurations and recognition of simple underlying trends during the 19th century. Arrhenius neutron absorption cross-sections up to two orders of magnitude less than subsequently suggested a local ordering and self-assembly mechanism other nuclei with similar masses. These were labelled magic numbers by of positive and negative ions illustrated by the presence of hydrogen, Eugene Wigner. The first three numbers are created by the 1s state (n = 1, l carbonate, sulphate, hydroxide and ammonium compounds. Following the = 0) which can contain up to 2 neutrons or protons followed by the 1p state discovery of the inert gases by Ramsey the table was extended to include which can contain up to 6 neutrons or protons giving 8 and the 1d and 2s an extra column though the position of hydrogen remained and still remains being close enough to overlap with each other to form the next shell of 2 + a source of debate within chemists. Seaborg not only extended the table by 6 + 10 + 2 which is the number 20, the next magic number. discovering numerous transuranic elements and several isotopes but also developed the concept of the Actinides, similar to the set of Lanthanides, At this point spin-orbit coupling between the orbital angular momentum above them within the table. The issue of how to construct a sequential and spin angular momentum comes into play. In Condensed Matter the sequence of atomic numbers throughout the table, having been observed origin is magnetic and the effect small requiring a minor correction. In the initially in theory by van den Broek and established experimentally by case of nuclear binding, the effect is about 20 times larger and is a property Moseley, remains to this day. Janet addressed the issue with his Left Step of the nuclear potential itself with a term proportional to L.S (orbital angular Periodic Table but the properties, particularly of hydrogen and helium, momentum and spin angular momentum). A feature of this type of coupling known at the time excluded any acceptance in general. Mass number though is that states with higher j have lower energy. essential in quantitative calculations remains an enigma/anomaly as to its The result is that the f (7/2) state containing 8 states overall arising role in any underlying fundamental mechanism; despite the introduction of from the next shell forms a separate shell itself giving 28 as the next magic the concept of isotopes and a prediction of a particle – the neutron – by number. Subsequent shells of 50, 82 and 126 appear to be structured Soddy and its subsequent discovery by Chadwick in 1932. Mendeleev in similarly where the highest j value of the next n value of quantum states the original construction of the table had to superimpose the significance of overlaps the previous n value of states, completing the shell and creating atomic number over and above that of mass number. the stability of the magic numbers. This is the classical Nuclear Shell The Nuclear Shell Model was proposed by Dmitry Ivanenko in 1932 Model at work. In this model the question as to why two sets of magic and developed independently by Maria Goeppert-Mayer, Eugene Paul numbers appear independently one for neutrons and one for protons and Wigner and J Hans D Jensen in 1949. It envisages each neutron/proton in what order remains unanswered. The assertion that magic numbers in themselves universally create a stable configuration has to be tempered to be moving in some potential and describes the energy levels in terms of 10 56 quantum numbers n, l, j similar to the wavefunctions of individual electrons by the transient existence of He and Ni and maybe other doubly magic as classified in Condensed Matter since both neutrons and protons nuclear configurations. Topology, quantum confinement and the fact that together with electrons are fermions. When the potential is approximated neutrons and protons are composite particles that can oscillate between fermionic and bosonic states may play a role in whatever space/time/ *Address for Correspondence: John O Roberts, Researcher, Former Open geometric evolves to accommodate such variations. University Tutor, UK, E-mail: [email protected] The Standard Model developed in the 1970’s as the result of discoveries Copyright: © 2020 Roberts JO. This is an open-access article distributed of large numbers or a zoo of elementary particles. Quarks was a name under the terms of the Creative Commons Attribution License, which permits coined by Gell-Mann having proposed the Eightfold Way; a method to unrestricted use, distribution, and reproduction in any medium, provided the organise hadrons along with Yuval Ne’eman in 1961. Subsequent theories original author and source are credited. by Weinberg, ‘t Hooft and others combined with experiments led to the Received 03 April 2020; Accepted 20 April 2020; Published 25 April 2020 discovery of three generations of quarks; to the prediction of Z, W, and Roberts OJ J Material Sci Eng , Volume 9:1, 2020 Higgs bosons with their discoveries in 1983(Z, W) and 2012(Higgs) and condensed matter and 10-18 to 10-20 m for plasma where the strong and weak to the merger of the electromagnetic and weak forces at high energies. forces began to couple with the electromagnetic force. The all-pervasive Another parameter – colour – extended the range of particles via quantum force of gravity mysteriously yet inevitably remained poised to act. One of chromodynamics following the appearance of a three-part structure for the the pairs of zeros generated by such sequences could be interpreted as a proton in Rutherford-type experiments. Other groups of particles include cut-off point for electrons in the condensed matter phase while the other leptons – electrons, muons and tau with their cousins; the electronic would be an infinite separation of protons/nuclei in the plasma phase caused neutrino, muonic neutrino and tau neutrino. All particles have their own anti- by the recycling of material from previous supernovae. Classifications of particle within a mathematical framework of U (1) x S U (2) x S U (3) group supernovae came and went – the patterns within the table were dominant. symmetry. Any such table appeared not to require mass number in its structure. This was only an average value of all the isotopes of a particular element at The theory lays out; six quarks, six leptons, four force carriers for the any one time. It must surely change in the 40th, 50th or even higher order four forces in Nature and the Higgs boson. Particles are now thought to be decimal place constantly as radioactive decay proceeded. The idea of excitations of interacting fields within quantum field theory. different ratios of isotopes for each element being created unique to each supernova confirmed the intuitive leap to omit mass number from the table. Questions The question of the source of radioactivity itself coupled with the range of time-scales for half-life for each radioactive nucleus remained an open one. • Why do neutrinos have mass and can mix – oscillate from one Such was the intensity of thought in the period 2011-2015 linking the type to another? idea of proton-proton interactions to produce neutrons or electron capture • What is Dark Matter? Does it exist? Does it require further particles to produce neutrons – a change of an up quark to a down quark with a or is it a property of gravity? myriad of possible outcomes illustrated by Feynman diagrams that the role of nucleosynthesis was overlooked. The Standard Model and beyond • Why is there so little anti-matter in the Universe? became the final destination. Magic numbers were considered but their role • Why is the Universe accelerating – if at all? at that time was not identified such was the thrust towards higher energies – second, third generation quarks and the newly discovered Higgs particle. • Having confirmed the existence of gravitational waves, what is a Cosmology and its applications to particle physics entered the arena. By graviton’s characteristics? 2015 the mind had reached a confusion of infinities similar to the explosion • What is the source of space-time? of ideas in that initial moment of 2010.